You see a sale price and the discount percentage, and you want to know what the item cost before the discount. This is a reverse percentage problem.
Original Price = Sale Price ÷ (1 − Discount Rate)
Why This Works
If an item is 30% off, you're paying 70% of the original price (100% − 30% = 70%).
So: Sale Price = Original × 0.70
To reverse it: Original = Sale Price ÷ 0.70
Examples
Example 1: You paid $63 after a 30% discount
You paid 70% of the original (100% − 30%)
Convert: 70% = 0.70
Original: $63 ÷ 0.70 = $90
Example 2: A phone costs $680 after 15% off
You paid 85% of the original (100% − 15%)
Convert: 85% = 0.85
Original: $680 ÷ 0.85 = $800
Common Mistake
Don't just add the discount percentage back to the sale price.
If you paid $70 after a 30% discount, the original is NOT $70 + 30% of $70 = $91.
The original is $70 ÷ 0.70 = $100.
Check: 30% of $100 = $30, and $100 − $30 = $70. ✓
💡 Always verify: Take your answer, apply the discount, and see if you get back to the sale price. If not, something went wrong.
🎯 Practice Problems
1. You paid $60 after a 20% discount. What was the original price?
A) $72
B) $75
C) $80
D) $48
2. A laptop is $850 after 15% off. What was the original price?
A) $977.50
B) $1,000
C) $900
D) $1,133
3. You paid $45 after a 10% discount. What was the original price?
A) $49.50
B) $55
C) $50
D) $40.50
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🎯 Bonus Practice
1. A coat costs $105 after 25% off. What was the original price?
A) $130
B) $140
C) $131.25
D) $126
2. You paid $36 after a 40% discount. What was the original price?
A) $50.40
B) $76
C) $60
D) $90
3. A pair of shoes costs $56 after a 30% discount. What was the original price?
A) $72.80
B) $80
C) $186.67
D) $70
4. Why can't you just add the discount percent back to the sale price?
A) You can — it gives the same answer
B) Because the discount was calculated from the original, not the sale price
C) Because you need to subtract instead
D) Because discounts don't work with percentages
5. An item is $180 after 50% off. What was the original price?